https://www.pcgamer.com/blizzard-reveals-world-of-warcraft-classic-pvp-content-plan/

Blizzard said last month that World of Warcraft Classic will be rolled out in six phases after it goes live this summer, based on the way-back-when update schedule of the original game. Today it expanded on that with details about its content plan for PvP, which will also follow the original WoW release pattern—which is to say that there won't be a "formal PvP system" in WoW Classic when it launches.

You'll still be able to kill your fellow players, though, and entirely without penalty, because no PvP system means no Dishonorable Kills—until the second phase of Classic rolls around, which will introduce the Honor System and PvP Rank Rewards. Those rewards will be the versions from the 1.12 patch, but won't be easy to get: Blizzard warned that "it will require a substantial time investment to rank up through the Honor System."